Phd Wharton
The Binomial Option Pricing Formula
Chapter 2 The Binomial Option Pricing Formula
2.1 Introduction
“Binomial option pricing is a simple but powerful technique that can be used to solve many complex option-pricing problems. In contrast to the Black-Scholes and other complex option-pricing models that require solutions to stochastic differential equations, the binomial option-pricing model is mathematically simple.”
The most widely used numerical method in the world for pricing American options is the Binomial Option pricing model, however, at the limit, a Binomial tree with a extensive number of steps is equivalent to the Black – Scholes formula used when pricing European options.
“Although slower than the Black-Scholes, it is considered more accurate,”
The model was developed in 1976, three years after the Black – Scholes formula by Mark Rubinstein, John Cox and Stephen Ross.
Mark Rubinstein was born June 8th 1944 in Seattle USA, in 1971 Rubinstein was awarded his PhD in finance from the University of California, Berkeley. Originally interested in equilibrium pricing models, Rubinstein became fixated with the splendor of option pricing theory and spent the next 20 years working principally on derivatives and hedging problems. In 1981 with the assistance of Hayne Leland and John O’Brien, Rubinstein launched a portfolio insurance firm Leyland O’Brien Rubinstein Associates that applied their options to revolutionise portfolio management by popularising the use of dynamic replication strategies that was extremely successful
“ we succeeded beyond my most optimistic imaginings. Unfortunately, we may have been too successful for our own good; our investment strategy was credited with causing the 1987 Stock Market crash.”
John Cox obtained his PhD in finance from the Wharton School at the University of Pennsylvania in 1975. Cox “is one of the world’s leading experts on options theory,” he is also one of the inventors of the Cox – Ingersoll – Ross model for interest rate dynamics. Cox was the winner of the International Association of Financial Engineers Financial Engineer of the Year in 1998, and is currently the Nomura Professor of Finance at MIT Sloan School of Management.
Stephen Ross was born in 1944. Ross received his Doctorate of Economics from Harvard University in 1970, Ross is best known for the development of the arbitrage pricing theory in the mid 1970’s, and he was also a major contributor to the creation of the Cox – Ingersoll – Ross model for interest rate dynamics. Ross has also served as President of the American Finance Association in 1988, and he won the prestigious International Association of Financial Engineers Financial Engineer of the Year in 1996.
About the Author
The author graduated with a BSc Hons in Mathematics from the University Of St. Andrews before moving to Heriot Watt University in Edinburgh where he attained an MSc in Applied Mathematics. The author is also an associate member of the Institute of Mathematics and its Applications. During his study and since leaving university the author has held a number of customer services and marketing roles within major retail organisations.For a free marketing course visit http://www.scottemcclelland.info
Scott E McClelland MSc Applied Mathematics AMIMA.
Authors Homepage: http://www.whoisscottemcclelland.info/
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